1. IntroductionMaterial selection is crucial in many engineeringprojects as it can determine the durability, cost, andmanufacturability of final products. In addition, dueto increasing regulations by government organiza-tions, manufactures are required to minimize envi-ronmental impacts of their processes and products.In fact, material selection can be pivotal for envi-ronmental concerns as recyclability and/or the end-of-life disposal methods vary from one choice ofmaterial to another. In today’s integrated designprocesses (IDP), a systematic selection of the bestmaterial for a given application begins with indenti-fying multiple mechanical/electrical/chemical/ther-mal properties, environmental impact factors, and

life cycle costs of candidate materials (Figure 1). Inessence, IDP requires design teams from differentdisciplines to work together from the project onsetto develop solutions that have multiple benefits.When multiple criteria from different disciplinesare to be satisfied in a material selection problem,however, complexities often rise with regards tocriteria conflicts and/or the importance of each cri-teria/discipline. Also, expert knowledge becomesfundamentally important to define correct indiceswithin each discipline. For example, the leaf spring/beam of a wing spar may be desired to be light andat the same time strong to support a given bendingload without deflecting excessively. The beam mate-rial selection problem is then considered as an opti-

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Multiple criteria decision making with life cycle assessmentfor material selection of compositesA. S. Milani*, C. Eskicioglu, K. Robles, K. Bujun, H. Hosseini-Nasab

School of Engineering, University of British Columbia, Okanagan Campus, Kelowna, BC V1V 1V7, Canada

Received 25 January 2011; accepted in revised form 25 June 2011

Abstract. With the advancement of interdisciplinary approaches in today’s modern engineering, current efforts in optimaldesign of composites include seeking material selection protocols that can (1) simultaneously consider a series of mechan-ical/electrical/chemical cost criteria over a set of alternative material options, and (2) closely take into account environmen-tal aspects of final products including recycling and end-of-life disposal options. In this paper, in addition to a review ofsome recent experimental and methodological advances in the above areas, a new application of multiple criteria decisionmaking (MCDM) is presented to deal with decision conflicts often seen among design criteria in composite material selec-tion with the help of life cycle assessment (LCA). To show the application, an illustrative case study on a plastic gear mate-rial selection is conducted where the cost, mechanical and thermal properties along with environmental impact criteria areto be satisfied simultaneously. A pure plastic gear is compared to a Polyethylene terephthalate (PET)/aluminum-powdercomposite alternative. Results suggest that simple MCDM models, including a signal-to-noise measure adapted to MCDMin the same case study, can be used to explore both trade-offs and design break-even points in large decision spaces as thedecision maker’s perspective over environmental, material performance and cost attributes change during the designprocess. More advanced topics including the account of material data uncertainties are addressed.

Keywords: polymer composites, material selection, multiple criteria decision making, life cycle assessment, sensitivityanalysis

eXPRESS Polymer Letters Vol.5, No.12 (2011) 1062–1074Available online at www.expresspolymlett.comDOI: 10.3144/expresspolymlett.2011.104

*Corresponding author, e-mail: abbas.milani@ubc.ca© BME-PT

mization problem where the density, !, should below while the elastic modulus, E, should be highenough to bear the load without exceeding a givenmaximum allowable deflection. It maybe assumedthat the beam’s length and width are constant andonly its thickness can vary to accommodate thedesign objectives. The simultaneous formulation ofthe beam’s mass and elastic deflection as a functionof the thickness gives a material performance index(i.e., a combination/ratio of the material properties)as E1/3/!. This index should be maximized duringthe material selection process; see [1] for more the-oretical details. If during decision-making themechanical design group in the project uses thedensity and stiffness as individual material proper-ties (and not as a ratio as defined above), less accu-rate or not application-specific results would beobtained.A number of recent experimental studies and selec-tion methods have been reported in the literature tohighlight the above multi-disciplinary nature ofcomposite material and product selection in IDP’s.Among these studies, those with a focus on environ-mental performance of composites are reviewed inSection 2. Research directions in relation to currentefforts in improving the recycling techniques ofcomposites are also addressed (Section 3). Next, anillustrative case study is presented in Section 4 ongear material selection with an emphasis on theapplication of multiple criteria optimization meth-ods and their appropriateness to explore trade-offsand break-even design points when cost, environ-mental and mechanical factors are simultaneouslytaken into account. A new signal-to-noise (S/N) con-cept in MCDM is also adapted in the same casestudy. Concluding remarks are included in Section 5.

2. Composite design and material selectionwith environmental considerations:A review

In recent years, there has been an increasing trendin the use of composite materials primarily in theaerospace and transportation industries. In compar-ison to traditional materials, composites offer higherstrength to weight ratios, non-corrosive properties,dimensional stability and good conformability. Togive a few examples, percentage weight of compos-ites has increased from 3% in Airbus A320 to over20% in A380. Similarly, Boeing uses over 50% ofcomposite materials in its 787 aircraft (for morespecific examples of current applications of fiber-reinforced composites in the aircraft industry, seethe study [2]). Similarly, composite materials haveplayed key roles in reducing the magnetic, acoustic,hydrodynamic, radar, thermal signatures, as well asincreasing payload, top speed, and operation rangein marine structures [3].Next to the above-mentioned superior physical andmechanical properties, recent studies show thatcomposites can increase savings of emissions to theenvironment, in particular in transport industries,when compared to more traditional structural mate-rials such as aluminum [4]. In air transport, emis-sions can be more environmentally damaging thanthose at ground level due to increased interaction ofstructures with gases at high altitudes. Scelsi et al.[4] through a life cycle assessment (LCA) analysison a set of actual aerospace components showedthat commercial fiber-reinforced composites suchas GLARE yield substantial reductions in overallenvironmental impact during the use stage (e.g.,240 000 km of flight distance). This is despite thefact that composites are more energy intensive tomanufacture and more difficult to dispose com-

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Figure 1. Schematic of material selection in an integrated design process

pared to traditional materials such as aluminum. Toaddress the latter gap/difficulty, numerous researchgroups have launched state-of-the-art projects todevelop more environmentally friendly compositessuch as natural fiber-reinforced polymers.Holbery and Houston [5] describe applications ofnatural-fiber-reinforced polymer composites inautomotive components. Their work suggested thatnatural fibers in composites yield high quality com-posite products while minimizing environmentalimpacts. Namely, fibers such as flax, hemp, andkenaf were tested and compared to more traditionalcomposites (such as glass fibers) to demonstrate thecompetence of the natural counterparts. Nonetheless,it was concluded that there still exist challenges toovercome in this field, including moisture stability,fiber-polymer interface compatibility, and consis-tency of fibers. Mechanical properties and biodegrad-ability of green composites (as linked to environ-mental factors) have also been studied experimen-tally by Shibata et al. [6]. They scrutinized a set ofcomposite laminates composed of regenerated cel-lulose (lyocell) fabric and three types of biodegrad-able polyesters [poly(3-hydroxybutyrate-co-3-hydroxyvarelate) (PHBV), poly(butylene succinate)(PBS), and poly(lactic acid) (PLA)]. The polyester/lyocell composite specimens were made of com-pression molding and examined for the effect ofnatural fiber content on their tensile moduli andstrengths, as well as Izod impact resistance. In addi-tion, biodegradability of the specimens were com-pared via a 120 day soil viral test and the order ofhighest to lowest biodegradable polyester/lyocellcomposite was found to be: PHBV > PLA > PBS.Regarding mechanical properties, at the same fibercontent the order of candidate materials was as fol-lows. Tensile moduli of PLA composites was higherthan those of PBS and PHBV composites, whereasPBS composites had higher tensile strength thanPHBV and PLA specimens. In view of MCDM, aclear indication of these results is that for each cho-sen design/ material selection criterion, a differenttop candidate can be nominated (i.e., the presenceof conflicting criteria in choosing a final material).Netravali et al. [7] presented a set of experimentsintended to compare the mechanical performance ofenvironmentally friendly (green) composites to com-mon synthetic reinforced plastics. A modified soyprotein based matrix was used by creating an ‘inter-

penetrating network like (IPN-like) resin’ withmechanical properties comparable to those of com-monly used epoxy resin. The IPN-like soy protein-based resin was further reinforced using nano-clayand microfibrillated cellulose. Different fibers includ-ing high strength liquid crystalline cellulose, aramidand E-glass fibers in the modified resin were usedand the ensuing tensile and flexural strengths ofcomposites were tested. It was demonstrated thatthe green fiber alternative was very competent.Although the soy-based materials and cellulosewere fully biodegradable, challenges such as con-sistent quality and water resistance remained yet tobe overcome for full applications of green compos-ites.A formal LCA of biofibers as reinforcement in plas-tic transport pallets has been conducted by Cor-biere-Nicollier et al. [8]. They performed LCA inorder to analyze the possibility of using China’sreed (CR) fiber as a replacement for glass fiber(GF). The analysis considered the entire life cycleof the two candidate materials including energy use,efficiency of transportation, and disposal wastephase. A comparison of emissions of pollutants intoair, soil and water due the life cycle stages of thetwo materials was made (Table 1 only shows theemissions to the air as sample results). It was con-cluded that CR fiber could be an excellent alterna-tive given that its lifetime is greater than therequired minimum three years and over this perioda notable effect on the reduction of polypropylenecontent, reduction of energy to create fibers, andimproved fuel efficiency in transportation due tothe use of lighter material are achieved. The CO2emission from GF pallet was 33.1 kg more than CRpallet.Katz [9] compared the environmental load of fiber-reinforced polymer (FRP) reinforced pavements tothat of steel reinforced pavement. The studyaccounted for the entire life cycle of the pavements,from obtaining the material resources to disposal.The analysis was carried out using the Eco-Indica-tor 99©: the environmental performance indicatormethod for LCA and ecodesign. The study dividedthe life cycle of a given pavement reinforcementcandidate to three stages: erection, maintenance,and disposal (Table 2). Three types of carbon FRP’swere tested and they all showed a lower environ-mental burden than the steel alternative in the main-

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tenance stage, mainly due to the reduced cementcontent. However, at the disposal stage, the envi-ronmental load of the steel reinforced pavement, ascan be seen in Table 2, was found to be lower thanthat of FRP reinforced pavements (i.e., again anexample of a local criteria conflict in choosing thefinal/optimum material).

Life cycle assessment of fiber reinforced compos-ites (FRCs) has been extensively discussed by Umair[10]. After a review of the history of FRCs and ageneral classification of their constituents, a num-ber of prominent applications of composites hasbeen discussed in construction, aerospace and mili-tary, transportation, medical sciences, sports goods,musical instruments, household products, energyproduction, and marine industries. Subsequently, apossible method to analyze the life cycle of FRCswas developed and exemplified for lightweightmaterials selection in ship construction. Three can-didate superstructures were compared: steel, bal-sawood core, and Polyvinyl chloride (PVC) foam.The life cycle of each superstructure was divided intomanufacturing, maintenance, and scrapping stagesfor a total service life of 25 years. Considering theglobal warming, acidification, and abiotic depletioncriteria, it was found that at the end-of-life stage ofthe LCA (Table 3), the steel structure would con-tribute most negatively to the environment. The pro-duction stage of the PVC structure would presentthe largest environmental impact due to the glasscontent in the insulation and in the face material.The Centre for Design at the Royal MelbourneInstitute of Technology or RMIT University hasprovided a technical report [11] on material selec-tion strategies for sustainable product development.Among other examples, the report discussed theneed for change in the economic and environmentalimpacts of the textile and fiber industry and maderecommendations for improved resource manage-ment. Current textile production methods, for mostpart, cause resource depletion and excessive waterconsumption, as well as pollution through toxic

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Table 1. Comparison of emissions of pollutants into air forglass fiber and China reed pallets [8]

Substance Unit GF pallet CR palletMaleic anhydride [mg] ! 5.88Benzo[a]pyrene [µg] 84.1 57.8Cd [mg] 32.7 26.8CO [g] 74.3 54.6CO2 [kg] 73.1 42.0Cr [mg] 8.53 4.92Cu [mg] 45 28.6Dimethenamide [mg] ! 36.9Glyphosate [mg] ! 38.7H2S [mg] 80.6 28.3HCl [g] 4.48 3.65HF [mg] 506 201.0Hg [mg] 1.48 0.68Methane [g] 150 79.4Mn [mg] 36.6 24.3N2O [g] 1.96 2.2NH3 [g] 0.123 11.3Ni [mg] 142 88.6NMHC [g] 497 318NOx [g] 513 349P [mg] 5.19 2.27Particles [g] 57.5 35.1Pb [mg] 195 56.2Pendimethaline [mg] ! 34.6SOx [g] 289 163V [g] 1.16 0.731Zn [mg] 512 375

Table 2. Comparison of environmental loads (expressed in Eco-indicator 99 points) of alternative pavements [9]; n repre-sents a given number of maintenance activities

Table 3. Comparison of environmental impact data for three ship superstructures with different waste disposal scenarios [10]

Slab type Erection Maintenance Disposal Total Relative load [%]Steel reinforced pavement 179000 n·13200 6020 291000 100FRP reinforced pavement 1 114000 N/A 7680 122000 44FRP reinforced pavement 2 117000 N/A 7680 124000 45FRP reinforced pavement 3 134000 N/A 9310 144000 52

Impact categories Balsa core sandwich super structure PVC sandwich foam super structure Steel super structureLandfill Incineration Recycle Landfill Incineration Recycle Recycle

Global warming (in kg CO2 eq.) 0.127 0.127 0.127 0.128 0.128 0.128 0.152Acidification (in kg SO2 eq.) 0.000943 0.000943 0.000943 0.000951 0.000951 0.000951 0.00113Abiotic depletion (in kg Sb eq.) 0.0111 0.0111 0.0111 0.0112 0.0112 0.0112 0.0133

chemicals. The study found that environmentalimpacts during all phases of fabric production canbe reduced with changes in the use of renewable/recyclable crops, increased product life, optimiza-tion of water systems and reduced waste produc-tion.Giudice et al. [12] described a new method of mate-rials selection in the life-cycle design process byintegrating mechanical and environmental perform-ance criteria. Their method utilized a multi-objec-tive analysis technique to show the application ofthe approach for material selection of a car brakedisk. The considered decision parameters were cost,environmental impact, and mechanical perform-ance. The candidate materials were grey cast ironBS 350 and F3K20S Duralcan (aluminum matrixcomposite). Limiting factors such as mechanicaldesign thresholds, geometry constraints, and feasi-bility of manufacturing methods for each candidatematerial were accounted for. Next to formulatingenvironmental impact indices for the problem, anoriginal step was taken in their work to incorporatecomputer aided design tools (including finite ele-ment method/FEM) into the multi-objective deci-sion model, thus avoiding the need for physicalexperiments in the early stages of decision-making.In fact, the use of FEM models in complex struc-tural material selection problems automaticallyensures the use of application-specific criteria val-ues, which otherwise would have to be found throughdefinition of performance indices as described inSection 1. For complex parts with nonlinear mate-rial and/or geometries, defining such indices analyt-ically can be a very difficult task.A multi-criteria decision matrix along with a greyrelational solution method was developed by Chanand Tong [13] to choose the best materials for avacuum cleaner dustbin. The candidate materialswere analyzed with respect to their cost, impact onthe environment and human health, and disposalmethods. A weight (importance factor) was given toeach criterion, but the weights could change depend-ing on who makes the analysis (i.e., a subjectiveweighting method was adapted). Three types ofmaterials were nominated: aluminum alloy (AL),acrylonitrile butadiene styrene (ABS) and polyure -thane (PU). For the end-of-life (EOL) disposal stage,four strategies were taken into consideration: reman-ufacturing/reuse (REM), recycling (REC), incinera-

tion with energy recovery (INC), and disposal tolandfill (LND). Subsequently, a grey coefficient wascalculated and assigned to each combination ofmaterial-disposal options (e.g., ABS with recycling).The coefficients (scores) made it possible for thedecision-maker to rank the candidates as shown inTable 4. The higher the coefficients, the better theoption in relation to the EOL treatment.A systematic comparison of LCAs of compressionmoulded wood-fiber-reinforced polypropylene com-posite sheets with that of pure polypropylene is dis-cussed by Xu et al. [14]. They introduced a newanalysis index called ‘material service density’,which is defined as the volume of material satisfy-ing a specific strength requirement. In contrast, forthe cases where the volume of a part is fixed, theyused the notion of ‘volume functional unit’. Two setsof LCA were conducted on the wood-fiber-rein-forced composites with 10, 30, and 50% levels offiber (mass) contents and the pure polypropylene. Itwas concluded that when material service density isused as a functional index during decision-making,wood-fiber-reinforced composite demonstrates supe-rior environmental friendliness compared to poly -propylene. Authors also discussed that environmen-tal loads of natural fiber reinforced composites candecrease with sufficient evidence when the use phaseof the design is focused on. In other words, it is ofutmost importance for material designers to notethat the use of natural fibers in composite materialsdoes not automatically make them ‘sustainable/ envi-ronment friendly’ unless the use phases (i.e., trans-portation) can justify that. It is the light density ofnatural fiber reinforced polymer products thatmakes them very attractive alternatives regardingtheir environmental impact during the use stage. Ifthe material production phase is taken into accountonly, which often includes cultivation, pesticidesand other types of chemical by-products, the envi-

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Table 4. The EOL grey relational grades for candidatematerials of a vacuum cleaner dustbin [13]

Ranking EOL order pair Grey relational grade1 ABS-REC 0.77082 AL-REM 0.69203 ABS-INC 0.50834 ABS-LND 0.50815 AL-REC 0 0.48636 PU-INC 0 0.38467 PU-LND 0.3647

ronmental standing of natural fiber composites com-pared to their counterparts made of synthetic fibersand resins is not conclusive. The energy regainobtained during recycling phase of green compos-ites also plays an important role in the LCA analy-sis.

3. RecyclingWhile at the design stage, decision-making modelsare considered as powerful mathematical tools toassess the performance of different existing com-posite options against more traditional material alter-natives, from the reviews presented in Section 2 andrelated patents such as [15], it is clear that a signifi-cant research interest is currently on the develop-ment of green composites composed of natural fibers(such as wood, bagasse, rice straw, and pine fibers)and/or biodegradable polymers such as polygly-colic acid (PGA) and cellulosic plastics. Some ofthe main challenges in this area remains to be thehigh cost of production, moisture stability problemsduring storage and utilization, quality consistencyin produced composites, and effective couplingagents between fibers and polymer [16, 17]. Furtherresearch is needed before these new genre of com-posites can fully replace current synthetic compos-ite constituents. At the same time, improving recy-cling techniques of synthetic composites is a keyfactor to address environmental aspects of usingthese materials and also landfill use restrictions thatare increasingly faced by different composite man-ufacturers. Recycling technologies for thermosetcomposites is extensively reviewed in the reference[18]. The major problem with recycling these mate-rials is the existence of cross linked molecules inthe polymer. Some reported recycling processesinclude pyrolysis, use of thermal fluidized bed, andgrinding. The LCA and recycling techniques ofthermoplastic composites such as PE, PP, PS andPVC, technical challenges along with their eco-nomic merits can be found in other studies such as[19, 20]. The most commonly used technique is per-haps mechanical recycling, when compared to chem-ical, physicochemical or energy recovery recycling.In the mechanical method, plastics from industrialwaste undergo sorting, shredding and washingprocesses to yield plastic flakes, pellets or powderthat can be reused in the manufacturing of newproducts, e.g., via extrusion. It is shown that recy-

cled composites can significantly reduce environ-mental impact during the materials acquisition andprocessing phases compared to conventional virginthermoplastics [20].Remark: It is worth adding that although over thepast decade some of the recycling processes of syn-thetic composites along with the development ofnatural composites have proven to yield highamounts of recyclates and save significant environ-mental loads, there still seems to be a need for moreimminent demand in market in order to achievetheir cost effectiveness across composite sectors formass production. The actual case studies such as[21] show that the recycling of composites wouldnot be cost-effective for companies unless there aredramatic changes to recycling policies or cost ofpetroleum.

4. An illustrative example on gear materialselection: A new application of signal-to-noise

This case study is primarily intended to illustratethe application of MCDM by which concerns aboutmultiple conflicting criteria can be formallyaddressed into an interdisciplinary material selec-tion process. MCDM, also often referred to as mul-ticriteria optimization, is particularly useful for thecomparison of a finite set of different alternatives/scenarios against a set of decision criteria [22].Both qualitative and quantitative values, monotonicand non-monotonic criteria, design tolerances,along with both objective and subjective weightingfactors from individual or group of decision makerscan be incorporated into such solution methods.Different types of MCDM models have been alreadyemployed in the past decade for material selectionproblems concerning mechanical properties, costand manufacturing criteria; see [23] for a state-of-the-art review.In the early stage of a design, more general methodssuch as Ashbey’s material selection charts can beused to identify a range of possible material solu-tions/candidates given an application. Alternativelyscreening methods, such those reviewed in [23],can be applied to shortlist a large pool/table ofmaterial candidates. In the simplest form, thescreening process may involve defining a mini-mum/threshold value for each decision criteria. Acandidate material is shortlisted only if it passes all

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the criteria thresholds. As such, all the screenedcandidates are considered feasible solutions, yetthey should be ranked from top to bottom for a finaldecision at the end of the design process. For thelatter ranking, MCDM methods such as the weightedsum method (WSM), TOPSIS, ELECTRE can beused [24]. No or little effort has been made to for-mally incorporate the above powerful decisionmaking tools in material selection problems in thepresence of LCA criteria. The selection techniquesemployed in the studies [12] and [13] can be indenti-fied within this category of models.To exemplify the application of MCDM in theintended case study, let us take two different gearmaterial options along with their cost, thermal andmechanical performances, and environmentalimpacts. The given material options are pure poly-ethylene terephthalate (PET) and a composite madeof 70% PET (i.e., with the weight fraction "PET =0.7) and 30% aluminum powder ("Al = 0.3). The

PET/aluminum powder composite (Figure 2) is anexample of the large variety of polymer-matrix/par-ticle filling composites that are widely used in mili-tary and civil applications [25]. The material cost,thermal and mechanical properties of each alterna-tive gear option are included in Table 5. Environ-mental impact of PET-Al gear is assessed by estab-lishing a life cycle shown in Figure 3. Subsequently,using the GaBi 4 software, an LCA analysis wasperformed based on three stages of life cycle: mate-rial production, transportation, and disposal/recy-cling. In Figure 3, the composite gear manufactur-ing facility receives PET (70% by weight) andaluminum (30% by weight) as raw materials whichweigh a total of 1 lb. Only 50% (0.35 lb) of the totalPET (0.70 lb) is new PET while the remaining por-tion (0.35 lb) is the recycled material according tothe recyclable fraction in Table 5. Similarly, only15% (0.045 lb) of the total aluminum (0.30 lb) isnew aluminum as the remaining weight (0.255 lb) iscomprised of the recycled material based on 85%recyclable fraction indicated for aluminum. In Fig-ure 3, in addition to manufacturing, two separatedisposal options are considered. Upon manufactur-ing and consumer use, 50% of the non-recyclableportions of the PET (0.175 lb) and aluminum(0.0225 lb), in other words the ‘solid waste’ gener-ated, are assumed to be incinerated while the remain-ing waste fractions (50%) are directed to a nearbylandfill. Similarly, the LCA analysis was repeatedfor the pure PET gear option.The obtained environmental criteria values fromLCA are added in Table 5 next to the mechanicaland cost criteria. It is assumed that the manufactur-

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Figure 2. Sample micrograph of aluminum powder in apolymer matrix (Tavman, 1996)

Figure 3. A basic life cycle of the PET-Al composite gear

ing cost and energy of the two material candidatesare comparable (at least for a low-scale production).The negative signs in the last column of Table 5indicate that the corresponding criteria are definedas cost-type (i.e., the lower the better) by the designer.The composite mechanical properties needed to beestimated from the volume fraction of its con-stituents (i.e., PET and Al). To this end, a simplerule of mixture was used as Equation (1):

Pcomposite = vAl·PAl + vPET·PPET (1)

where P represents the property to be obtained inrelation to the percentage compositions of the con-stituent materials vAl and vPET are the volume frac-tions of the composite constituents and can be

related to their weight fractions based on Equa-tions (2) and (3) [26]:

(2)

(3)

where !composite is the density of the composite andis related to the density of the constituents as Equa-tion (4):

(4)

For calculating the effective longitudinal thermalexpansion coefficient of the composite, "composite,

1rcomposite

5mAl

rAl1mPET

rPET

mPET 5rPET

rcompositevPET

mAl 5rAl

rcompositevAlmAl 5

rAl

rcompositevAl

mPET 5rPET

rcompositevPET

1rcomposite

5mAl

rAl1mPET

rPET

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Table 5. Multi-disciplinary property values of candidate materials in the present case study

*For 1 lb of the PET gear, 50% of the material comes from the recycled fraction, thus the net cost is reduced by 50%.**For 1 lb of the composite gear, 50% of PET and 85% of Al come from the corresponding recycled fractions, thus the estimated cost is

adjusted.

Category Properties Al(Min)

Al(Max)

PET(Min)

PET(Max)

Al(Ave)

PETgear(Ave)

Compositegear(Ave)

NormalizedPET

properties

Normalizedcompositeproperties

± Factor

Cost Price [USD/lb] 0.6453 1.046 0.835 0.919 0.846 0.4383* 0.3449** –1 –0.7868 –

Mec

hani

cal-t

herm

al

Density [lb/in3] 0.0964 0.0986 0.047 0.051 0.098 0.0486 0.0572 –0.8494 –1.0000 –Young’s modulus[106 psi] 10.1 10.44 0.4 0.601 10.27 0.5004 2.2191 0.2255 1.0000 +

Elastic limit [ksi] 4.134 4.569 8.195 9.036 4.352 8.6155 7.8653 1 0.9129 +Tensile strength[ksi] 11.02 12.18 7.005 10.5 11.6 8.7525 9.2535 0.9459 1.0000 +

Hardness rockwell[R] 24.5 25.5 17 18.7 25 17.85 19.1079 0.9342 1.0000 +

Endurance limit[ksi] 3.046 3.336 2.802 4.2 3.191 3.501 3.4465 1 0.9844 +

Fracture toughness[ksi·in1/2] 27.3 31.85 4.323 4.778 29.58 4.5505 8.9530 0.5083 1.0000 +

Thermal conductiv-ity [BTU·ft/h·ft2·F] 118.4 123.1 0.08 0.087 120.8 0.0835 21.3119 0.0039 1.0000 +

Thermal expansion[#strain/F] 12.33 13 63.7 66.3 12.67 65 22.3901 –1 –0.3445 –

Max service temp[F] 266 392 152.6 188.6 329 170.6 198.4667 0.8596 1.0000 +

Envi

ronm

enta

l

Production energy[kcal/lb] 20500 22600 8624 9534 21560 9079 12823 –0.7080 –1 –

CO2 creation[lb/lb], 9.03 9.98 2.21 2.45 9.505 2.33 4.4825 –0.5198 –1 –

Recyclable fraction 0.8 0.9 0.45 0.55 0.85 0.5 0.605 0.8264 1 +Resources [lb/lb] 247.91 247.93 –0.9999 –1 –Emission to air[lb/lb] 240.82 240.75 –1 –0.9997 –

Emission to freshwater [lb/lb] 0.3375 0.32 –1 –0.9483 –

Emission to seawater [lb/lb] 0.0101 0.0101 –1 –1 –

Emission to indus-trial soil [lb/lb] 0.0001 0.0001 –1 –0.9663 –

the thermoelastic extremum principle yields [26](Equation (5)):

(5)

where EAL, PET, composite denotes, respectively, theYoung’s modulus of Al, PET and the composite(Table 1). Finally, for the composite environmentalfactors, a similar rule of mixture as in Equation (1)was employed by using the weight fractions inorder to be consistent with the Eco-indicator 99 val-ues.Next, properties within each category of cost, envi-ronmental impact, thermal/mechanical performanceare normalized using the two average values in eachrow (one for PET and one for the composite). Thenormalization is necessary since different proper-ties are of different units. To this end, each criterionvalue is divided by the maximum of the two mate-rial values. For example, for the elastic limit crite-rion, the (average) PET value is 8.6155 ksi and thecomposite value is 7.8653 ksi. The normalized val-ues, respectively, are calculated as 8.6155/8.6155and 7.8653/8.6155. For cost-type criteria, after theabove normalization, the values are multiplied by‘–1’ as seen in the grey cell (i.e., the final decisionmatrix) in Table 5.From the normalized decision matrix, where for allvalues the higher-the-better, one can notice thateach material option is superior to the other undersome particular criteria, but lacking under the restof criteria. To aggregate all the conflicting criteriavalues into one overall score, the well-knownweighted sum method (WSM) was used for eachmaterial; i = 1, 2 (Equation (6)) [22]:

Scorei = !!(cost)·NPj(cost)+!!(Mechanical-Thermal)·NPj (Mechanical-Thermal) + + !!(Environmental)·NPj(Environmental) (6)

where NPj refer to the normalized values and ! val-ues are the weights of the three categories of criteriafor the decision maker/designer. For instance, ifenvironmental impact is a major concern in a proj-ect, the weight of all criteria under this category

would have higher values than the rest of criteria. Inthe current example, a set of initial weights wasassumed as shown in Table 6. Based on theseweights and the equation above, the sub-total andthe total score of each material are calculated inTable 7. The overall score of the composite sug-gests that it should be ranked/preferred over thepure PET option. Also, for both materials, it is clearfrom the sub-criteria scores that the (negative) envi-ronmental load is the highest compared to themechanical/thermal and cost performance values.

4.1. Sensitivity analysisAfter an initial estimation of weights, it is often thecase that the designer/decision maker (DM) wouldbe interested to know how the trade-off betweencriteria categories plays a role on the final materialranking (sensitivity analysis). To this end, it wouldsuffice that the DM simply changes the relativeweight values (!) between the criteria groups andrecalculates the scores. Different weight combina-tions yield different material recommendations assummarized in Figures 4–6. Since here we havethree categories of criteria, for better visualizationpurposes, a mapping from three-dimensional Paretospace to the two-dimensional space has been usedby fixing the level of one weight at a time and plot-ting the effect of the variation of the other two onthe material scores. Also note that at each point, thesum of weights (cost, environmental, and mechani-cal-thermal) is the unity. For instance, in Figure 4a,given the cost weight of 10%, the summation ofmechanical-thermal and environmental criteriashould be 90%. That means, e.g., for the two points

1EPET

Ecomposite1vPET·aPET 2

acomposite5EAl

Ecomposite1vAl·aAl 2 1acomposite5

EAl

Ecomposite1vAl·aAl 2 1

1EPET

Ecomposite1vPET·aPET 2

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Table 6. Initial weights of different criteria categories basedon the designer/decision-maker’s viewpoint

Table 7. Scores for the PET and composite options usingthe weights in Table 6

CategoryCost Mechanical/Thermal Environmental

Weight 0.25 0.25 0.5

MaterialsCriteria categories

PET Composite

Cost –0.250 –0.196Mechanical/Thermal 0.907 1.638Environmental –2.700 –2.957WSM total score –2.043 –1.515

on the left corner of the plot, the mechanical-ther-mal criteria weight is 90% and the environmental0%.From Figure 4b one can conclude that at a highweight of cost (~50%), the composite material out-performs PET regardless of their differences in themechanical-thermal performance and environmen-tal impact values due to higher recyclability per-centage. From Figure 4a, however, one notices thatwhen the cost weight is low (10%), there is a ‘breakeven’ point (~15% mechanical-thermal, i.e., 75%environmental) where the ranking of the two mate-rial swaps. A similar break-even point can benoticed in Figure 5a regarding the cost and environ-mental criteria. The indication from this figure alongwith Table 7 is that a low cost can be achieved at theexpense of higher environmental impact and viceversa. For higher mechanical-thermal weights as in

Figure 5b, the composite is noticeably preferredover PET. Finally, from Figure 6, it is seen that thecomposite can outperform the PET alternative withno break-even point for lower environmental weights(up to ~35%).

4.2. A signal-to-noise concept The WSM method in Equation (6) is perhaps themost common method among MCDM models inpractical applications [27]. It is important, however,to understand that this method is compensatory inthat the sub-scores of criteria (after normalizationand weighting) are added together to find a totalscore. As such, the decision maker/designer implic-itly agrees that a low value of one criterion can becompensated by a high value of another criterion inthe final decision-making. This should be true mostof the time for the type of applications outlined in

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Figure 4. The trade-off between the (thermo) mechanical and environmental criteria at different fixed cost criterion weights

Figure 5. The trade-off between the cost and environmental criteria at different fixed (thermo) mechanical criteria weights

Figure 6. The trade-off between the cost and (thermo) mechanical criteria at different fixed environmental criteria weights

this paper (selection of optimal composite product),but there may be cases where the designer wouldlike to limit this direct compensation among selec-tion criteria by means of their variability. To thisend, here we use a new concept based on a signal-to-noise (S/N) ratio for material selection.The definition of S/N may be based on the inverseof well-known ‘coefficient of variation (CV)’ in sta-tistics. CV, also known as unitized risk, is a normal-ized measure of dispersion which is found by divid-ing the standard deviation of a sample $ to its mean". Thus, the S/N score may be defined as "/$. Tounderstand this in the MCDM context, let us recallthe upper-level decision matrix of Table 7, wheresub-criteria within each category (environmental,mechanical/thermal, and cost) have been aggre-gated, but the designer may hesitate to sum the val-ues between groups of different criteria. To formal-ize this non-compensatory ranking preference, foreach material column in Table 7 one can find themean " and divide it by the standard deviation ofthe column $. For instance, for PET (Equation (7)):

= –0.369 (7)

Similarly, for the composite option we findS/N(composite) = –0.218. A larger signal to noise ratioshould be preferred. In essence this means, onewould like to chose a material that on average has ahigh score (") over all criteria but at the same timehas a low variation ($) among different categories ofcriteria. That is, ideally, the chosen material shouldbe good in all criteria. Given the above scores forthe two alternative materials in the present casestudy, the composite option outperforms the pureplastic material with the S/N non-compensatoryapproach.

5. ConclusionsIn today’s integrated design processes for compos-ite products, it is necessary to explore optimaldesign options by simultaneously analyzing mate-rial properties in a multitude of disciplines (mechan-ical, cost, environmental, etc). Next to the existingselection tools [28], MCDM models can providethe ability to formulate and systematically comparedifferent alternatives against large sets of design

criteria, thus giving engineers a versatile tool totackle complex decision-making tasks. To show anapplication of a well-known MCDM method (namelythe WSM) in a relatively large-scale decision space(with one cost, seven environmental, and elevenmechanical/thermal attributes), an illustrative exam-ple was presented in a plastic gear material selec-tion problem. A pure PET gear was compared to acomposite PET/aluminum-powder alternative. Theresults showed a higher total score for the compos-ite. It was also shown that the method can beemployed to explore criteria trade-offs and decisionbreak-even points by varying the designer’s weightsover different criteria categories. Similar MCDMmodels can be used by other practitioners to mathe-matically study the benefits gained and lossesendured during material development, replacementor selection of new products. In doing so, however,next to basic MCDM models such as WSM, it maybe worth investigating the application of moreadvanced methods that can include uncertaintiesboth in material datasets as well as designers/deci-sion makers’ opinions over criteria weights (see,e.g. [29] for an application of ELECTRE III andrevised Simos’ methods). Advanced MCDM meth-ods under uncertain/incomplete data can be particu-larly important for the LCA analysis of compositessince inventory databases in the commercial LCApackages are still not inclusive and modelingassumptions normally need to be made (as is thecase in several reported LCA studies includingthose reviewed in this article). The notation of com-pensation and non-compensations may be accountedfor during multi-disciplinary material selectionproblems. An application of a signal-to-noise con-cept was recommended in the present case study bydividing the average score of each alternative over adispersion measure showing the non-uniformity ofthe given material performance over different crite-ria categories. Finally, it should be pointed out thatfor more practical, real-world design scenarios, theanalysis of material candidates’ disposal options aswell as their recyclable percentages need to bealigned with waste management codes and regula-tions of both manufacturers and local authorities.Accordingly, next to the cost of raw material, theinclusion of production and disposal costs can bevital for a successful multiple criteria materialselection process.

S>N1PET25Average120.250, 0.907, 22.700 2

STD120.250, 0.907, 22.700 2 5S>N1PET25Average120.250, 0.907, 22.700 2

STD120.250, 0.907, 22.700 2 5

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AcknowledgementsFinancial support from the Natural Sciences and Engineer-ing Research Council (NSERC) of Canada as well as theUBC’s Work-Learn Program is acknowledged. The authorsare also grateful to the anonymous referees for their con-structive comments and suggestions.

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